P&L attribution by Greeks

On Sunday 1 Feb 2026, the Budget Day special session, the 24,850 Nifty straddle on the 24 Feb expiry settled at Rs 760.35. On Monday 2 Feb it settled at Rs 712.50. Nifty closed at 24,825.45 and then 25,088.40, a rise of 1.06%. A seller of that straddle made Rs 47.85 a unit on the day. The first question any trader asks is why. The honest answer has four parts and a remainder. That split is called P&L attribution, and it is how a book is told apart from luck.

The idea, plainly

An option's value moves because the future moved, because implied volatility moved, because a day passed, and because those effects are curved. The Greeks are the slopes of those moves (modules F21, I09, I10 and I12). Multiply each slope by the move it faces and the four pieces add up to an estimate of the day. What the estimate misses is the residual.

For a sold position every sign flips. Theta becomes a gain, gamma a loss, and vega a gain when implied volatility falls. A short straddle starts with almost no delta, so the interesting pieces are the other three.

The procedure

1. Take the Greeks of each leg at the start of the window, from Black 76 at the leg's own implied volatility.
2. Take the moves over the window: the future, each leg's implied volatility on the two dates, and the days.
3. Multiply, add by piece, and compare with the change in the settlement price.
4. Show the residual. Never fold it into a piece.

Worked example: one seller, three windows

The same exercise on three real windows, each a sold straddle at the strike nearest the future, priced from NSE settlement files. Window one is Budget Day to the next session, one day, on the 24,850 strike. Window two is 10 Jun to 16 Jun 2026, six days, on the 23,250 strike. Window three is 16 Jun to 29 Jun 2026, thirteen days, on the 24,000 strike. Values are rupees for one lot of 65 units.

The arithmetic of window one, line by line

The four pieces for window one, per unit sold. Delta of 0.018 on a move of 288 points gives −5.25. Gamma of 0.00083 a point, as half gamma times the move squared, gives −34.57. Theta of −16.42 a day for the long straddle, flipped for the seller and applied for one day, gives 16.42. Vega of 24.8 on the call times its volatility change of −1.84 points, plus 24.8 on the put times −1.24 points, flipped, gives 76.39. The total is 52.99, against an actual change of 47.85. The gap is −5.14.

Window one: a short step, well explained

The straddle settled at Rs 760.35 and Rs 712.50, and the future moved from 24,853.50 to 25,141.80. The call's implied volatility went from 15.6% to 13.8% and the put's from 15.0% to 13.8%, falls of −1.84 and −1.24 points. The seller was paid for one day of time, lost a little to gamma on the move, and was paid again because implied volatility fell. The vega piece was the largest, which is the lesson of the day: the seller's gain was mostly the fall in volatility after the Budget, not the passing of a day. The Greeks explain 111% of the actual figure, and the residual is a few hundred rupees a lot.

Window two: a big move, gamma dominates

The straddle went from Rs 643.70 to Rs 821.50. Over six days the future rose from 23,240.10 to 24,001.00, 761 points, and a short straddle with almost no delta pays for that through gamma. The gamma piece is the largest figure in the column. Theta and a fall in implied volatility, the call's from 15.1% to 13.7% and the put's from 14.6% to 13.6%, gave some back. The Greeks explain 78% of the loss. The rest is the size of the move: with a move of about three percent, vanna and volga have their say. This is the window of module A01's ledger, seen from the straddle.

Window three: the Greeks run out

The straddle went from Rs 453.30 to Rs 160.75. The future barely moved, from 24,001.00 to 23,972.90, so delta and gamma are close to nothing. The call's implied volatility went from 12.1% to 15.4% and the put's from 12.1% to 16.4%. The seller made Rs 292.55 a unit, but the Greeks at the start of the window explain only 23% of it. The missing parts are theta and vega, and both change fast as expiry comes close. Theta of −16.13 a day at the start is one number applied to thirteen days, and the real theta grew. Vega went the other way: the call's vega was 18.7 at the start and 5.0 on 29 Jun, so the vega loss was smaller than the start of window figure says.

Why the residual grows with the window

The Greeks are slopes at one point. The longer the window, the further the market travels from that point, and the more the slope has changed. Time is the clearest case: the at the money theta rose from Rs 16.13 to Rs 78.87 a unit a day for the 24,000 straddle, 4.9 times as much, between fourteen days to go and one, with implied volatility also higher, which adds to it. The fix is not a better formula. It is a shorter window: attribute daily, with the Greeks of that morning, and add the days up. A desk does this every evening. A trader with a position screen can do a rougher version, one day at a time, with the Greeks calculator.

A residual is information

People treat the residual as an embarrassment and tuck it into theta. That throws away the most useful number on the page. A residual that is small and random says the Greeks are doing their job. A residual that is large and always the same sign says something is missing: a skew move, a hedge priced at the wrong time, or a window that is too long. Window three is the third kind. Read the residual column first and the pieces second.

Try it on the grid

The scenario grid linked below reprices a position in full for index, volatility and time shocks. Pick the short straddle on the 10 Jun 2026 chain and set the days to five. Then switch the view to what the Greeks miss. You will see the Greek estimate and the full reprice side by side, with the miss largest in the corners, where the move in the index and the change in volatility are both large.

Units, signs and the volatility you use

Three slips account for most wrong attributions. The first is mixing per unit and per lot: the table above is per lot, the arithmetic line is per unit, and a lot is 65 units. The second is signs: every piece flips for a sold position, and a fall in volatility is a gain for a seller but a loss for a buyer. The third is the volatility. Each leg has its own implied volatility, so the call and put of one strike do not move together, and the strikes of one expiry do not move in step. Use each leg's own change, as the table does, and not one number for the position. India VIX and the 30 day figure in the chart move differently from a near expiry option, which is why the vega piece uses the leg and not the index.

From one position to a book

The pieces add across legs and across positions, so a book is attributed by adding each trade's pieces. Desks then cut the sum by expiry, by strike band and by strategy. A book that is short vega in the near expiry and long vega in the far one shows two different vega pieces that a single number would hide. The cut that matters most is by expiry, because near expiry options carry most of the gamma and theta (module A14). I would rather a trader show me a daily table with a visible residual than a clean story with none.

What attribution can and cannot say

• It says where the money came from. A week of profit that was all vega is a week of luck in volatility, not a pattern of skill.
• It does not forecast. The vega gain in window one came because implied volatility fell after an event. It tells nothing about the next one.
• It needs honest inputs. Settlement prices are NSE's, not fills. Add a bucket for trading costs and slippage, and keep it apart from the residual.
• It sums across a book. Greeks add across legs, and so does each piece. Module A14 uses the same pieces to size a book's risk.

The common mistake

The claim: My Greeks add up to my P&L, so I understand where it came from. They add up only when the window is short and the move is small. In the table above, the same method explained 111% of the day, 78% of the six day window and 23% of the thirteen day window. A figure that holds for one day and fails for thirteen is not a measurement of the position. It is a measurement of how stale the Greeks are. Keep the residual on the page, and shorten the window when it grows.

Key takeaways

• Attribution multiplies each Greek by the move it faces.
• The Greeks explained 111% of a one day window.
• The same method explained 23% of a thirteen day window.
• The residual holds higher order terms, strike moves and rounding.
• Straddle theta was 4.9 times higher on 29 Jun than on 16 Jun.
• A profit that was all vega is volatility luck, not a pattern.

Before you trade. Derivatives trading carries a high risk of loss. SEBI's study "Profitability of Individual Traders in the Equity Derivatives Segment (FY25 to FY26)" (August 2026) found that 87.7% of individual traders in equity F&O made net losses in FY26, with aggregate net losses of Rs 91,685 crore. Read the SEBI study